pyzernike.zernike_order_to_index

pyzernike.zernike_order_to_index(n: Sequence[Integral], m: Sequence[Integral]) → List[int]

Convert Zernike orders (n, m) to their corresponding indices in the OSA/ANSI Zernike polynomial ordering.

\[j = \frac{n(n + 2) + m}{2}\]

If \(|m| > n\) or \(n < 0\), or \((n - m)\) is odd, an error is raised.

See also

• pyzernike.zernike_polynomial() for computing the Zernike polynomial \(Z_{n}^{m}(\rho, \theta)\).

• pyzernike.zernike_index_to_order() for converting indices back to Zernike orders.

• The parameters n and m must be sequences of integers with the same length.

The first few Zernike polynomials in the OSA/ANSI ordering are:

j	n	m
0	0	0
1	1	-1
2	1	1
3	2	-2
4	2	0
5	2	2
…	…	…

Parameters:

• n (Sequence[Integral]) – The radial orders of the Zernike polynomials.

• m (Sequence[Integral]) – The azimuthal frequencies of the Zernike polynomials.

Returns:

A list of indices corresponding to the Zernike orders.

Return type:

List[int]

Raises:

• TypeError – If n or m are not sequences of integers.

• ValueError – If n and m do not have the same length.

Examples

from pyzernike import zernike_order_to_index

n = [2, 3, 4]
m = [0, 1, -2]
indices = zernike_order_to_index(n, m)
print(indices)  # Output: [4, 8, 11]